The event when the die lands on 6 on the fourth, fifth, sixth, and seventh seventh ​rolls but not on any of the other​ rolls can be represented by:

x1, x2, x3, 6, 6, 6, 6, x4

where x1, x2, x3 anb x4 are numbers from 1 to 5

The total number of different rolls that can occur is:

6^8

The number of the events where the dice lands on 6 on the fourth, fifth, sixth, and seventh seventh ​rolls, but not on any of the other​ rolls is: 

5*5*5*1*1*1*1*5 = 5^4

P(x1, x2, x3, 6, 6, 6, 6, x4) = 5^4/6^8

P(x1, x2, x3, 6, 6, 6, 6, x4) = 0.00037

The probability is 0.00037.